SAT subject mathematics Complex numbers

[lily]

SAT subject mathematics Complex numbers
Which of the following is equal to i^{2013}?
(A) i
(B) -i
(C) 1
(D) -1
(E) 2i

Thanks!:D

[miranda]

We know that for the imaginary unit i hold the following
i^2=-1,
i^3= i^2 \cdot i=(-1) \cdot i=-i
and i^4=(i^2)^2=(-1)^2=1.

Also, 2013 can be written as 4*503+1

So, i^{2013}=(i^4)^{503} \cdot i^1=1 \cdot i=i

Therefore the correct answer is (A).

Hope these help!!:)

[lily]

We know that for the imaginary unit i hold the following
i^2=-1,
i^3= i^2 \cdot i=(-1) \cdot i=-i
and i^4=(i^2)^2=(-1)^2=1.

Also, 2013 can be written as 4*503+1

So, i^{2013}=(i^4)^{503} \cdot i^1=1 \cdot i=i

Therefore the correct answer is (A).

Hope these help!!:)

Thank you:)